For those on a budget, consider traveling to Ireland via bus rather than via plane.  The bad side to this is that you waste a lot of time traveling.  

Eurolines offers the following routes from Ireland:

Via Dublin,
    Dublin - Birmingham - London (Day Service)
    Dublin - Manchester - Leeds
    Dublin - Glasgow - Edinburgh
    Galway - Westport - London

Via Rosslare,
    Tralee - Limerick - Waterford - London

European Services,
    Ireland - London - Paris
    Ireland - London - Amsterdam
    Ireland - London - Brussels
    Ireland - London - Baltic States
    Ireland - London - Warsaw - Bialystok
    Ireland - London - Stalowa Wola
    Ireland - London – Zamosc

For more information on buses please visit:
www.eurolines.ie
www.buseireann.ie
www.poloniatransport.pl (polish only)